Utilization of a thickness shear mode (TSM) quartz resonator as a mass characterization device for minute mass loadings, down to the nanogram level, is well established. Application of TSM resonators as thin-film thickness and density monitors, detectors of chemical compounds and contaminants in gaseous and liquid environments, and biosensors has been extensive over the last two decades (G. Sauerbrey. Z. Phys., vol. 155, pp. 206-222, 1959; R. M. Mueller and W. White, “Direct gravimetric calibration of a quartz crystal microbalance.” Rev. Sci. Instr., vol. 39, pp. 291-295, 1968; S. J. Martin, et al., “Characterization of a quartz crystal microbalance with simultaneous mass and liquid loading.” Analytical Chemistry, vol. 63, pp. 2272-2281, 1991; A. Menon, et al., “Coated-quartz crystal resonator (QCR) sensors for on-line detection of organic contaminants in water.” IEEE Trans. Ultrason., Ferroelect., Freq. Contr., vol. 45, pp. 1416-1426, 1998; A. Smith, “Gravimetric analysis of non-volatile residue from an evaporated droplet, using the quartz crystal microbalance/heat conduction calorimeter.” J. ASTM Intl., vol. 3, pp. 1-5, 2006; A. Smith and H. M. Shirazi, “Principles of quartz crystal microbalance/heat conduction calorimetry: measurement of the sorption enthalpy of hydrogen in palladium.” Thermochim. Actua., vol. 432, pp. 202-211, 2005; D. S. Ballantine, Jr., et al., Acoustic Wave Sensors: Theory, Design, and Physico-Chemical Applications. San Diego, Calif. USA: Academic Press, 1997). Typically referred to as a quartz crystal microbalance (QCM), a TSM quartz resonator consists of a quartz disk of the thickness of which depends upon the operating resonance frequency, with metallic planar electrodes deposited on both faces. Typical resonance frequencies are between 5 and 10 MHz (P. J. Cumpson and M. P. Seah, “The quartz crystal microbalance; radial/polar dependence of mass sensitivity both on and off the electrodes.” Meas. Sci. Tech., vol. 1, pp. 544-555, 1990; P. J. Cumpson, “Quartz crystal microbalance: A new design eliminates sensitivity outside the electrodes, often wrongly attributed to the electric fringing field.” J. Vac. Sci. Tech. A, vol. 15, pp. 2407-2412, 1997), with the resulting mass sensitivities in the nanogram range. All of the devices considered in this study were plano-plano AT-cut quartz Cr/Au electroded resonators having base operating frequencies of 5 MHz.
Deposition of mass, either in the form of a thin mass layer or point mass, that is inertially coupled to the device surface, causes a reduction in the resonance frequency, which is directly proportional to the minute mass deposited. However, an important limitation on the mass sensitivity of current TSM devices exists. Utilization of the Sauerbrey model to directly relate the frequency shift to mass loading requires that the mass be uniformly distributed across the surface plane of the TSM device. While the mass sensitivity distribution is quite non-uniform for typically utilized devices with circular electrodes, the Sauerbrey model agrees with experimental values within a percent or so, for uniformly distributed elastic films. The non-uniformity of mass sensitivity of current TSM devices is well documented (P. J. Cumpson and M. P. Seah, “The quartz crystal microbalance; radial/polar dependence of mass sensitivity both on and off the electrodes.” Meas. Sci. Tech., vol. 1, pp. 544-555, 1990; P. J. Cumpson, “Quartz crystal microbalance: A new design eliminates sensitivity outside the electrodes, often wrongly attributed to the electric fringing field.” J. Vac. Sci. Tech. A, vol. 15, pp. 2407-2412, 1997; M. D. Ward and E. J. Delawski, “Radial mass sensitivity of the quartz crystal microbalance in liquid media.” Analytical Chemistry, vol. 63, pp. 886-890, 1991); V. M. Mecea, “Loaded vibrating quartz sensors.” Sens. Actuators A: Phys., vol. 40, pp. 1-27, 1994; F. Josse, et al., “Analysis of the radial dependence of mass sensitivity for modified-electrode quartz resonators.” Analytical Chemistry, vol. 70, pp. 237-247, 1998). This non-uniformity devices is well documented, (F. Josse, et al., Analysis of the radial dependence of mass sensitivity for modified-electrode quartz resonators. Analytical Chemistry, 70, pp. 237-247, 1998; P. J. Cumpson, M. P. Seah, The quartz crystal microbalance; radial/polar dependence of mass sensitivity both on and off the electrodes. Meas. Sci. Tech., 1, pp. 544-555, 1990), and is attributed to the reduction in particle displacement amplitude extending from the center. At the device center, the resonating wave drives the quartz from all radial directions prompting maximum displacement and, consequently, mass sensitivity. Moving away from the center, the displacement amplitude tapers off with radial position producing a Gaussian-like distribution in the mass sensitivity P. J. Cumpson, M. P. Seah, The quartz crystal microbalance; radial/polar dependence of mass sensitivity both on and off the electrodes. Meas. Sci. Tech., 1, pp. 544-555, 1990). Further, the current mass sensitivity devices are susceptible to mechanical vibrations prompting instability and inaccuracies in measurements. Additional contributions to the non-uniformity of the mass sensitivity arise from the anisotropic structure of the quartz. Observed deviations in sensitivity measurements from other studies, sweeping multiple radial axes of the resonator from 0=0° to 90°, indicates that the wave propagation characteristics are notably different depending on the axis of motion in the quartz substrate (M. D. Ward and E. J. Delawski, “Radial mass sensitivity of the quartz crystal microbalance in liquid media.” Analytical Chemistry, vol. 63, pp. 886-890, 1991).
These deviations may be acceptable for mass measurement and material characterization of uniform films, but current resonator surfaces cannot confine liquid droplets within the area of constant mass sensitivity. Current analytical and mechanical mass balances are inadequate based upon their high costs and low mass sensitivity, limited to microgram measurement.
Although the studies were not explicitly driven towards reducing the effects of the anisotropy of piezoelectric substrates on the wave propagation and mass sensitivity profile, previous research has considered alternative quartz surface geometries including plano-convex, with the top face of the crystal convexly contoured and the bottom remaining planner, to eliminate the destructive coupling observed between the fundamental and flexural (parasitic) oscillating modes in plano-plano devices. For ‘n-m’ QCR devices, studies have shown that smaller electrodes and thicker electrodes result in more sensitive mass detection, as the larger mass traps the acoustic wave within the electroded region of the quartz crystal. Cancellation of the fundamental operating mode by these flexural modes upon the deposition of electrode mass on the plano-plano resonator device dampens the energy of the resonator prompting a lower quality factor, Q (E. Ansorge, et al., “Plano-convex shaped langasite microbalances for high temperature applications.” Proceedings, IEEE Sensors 2007, Atlanta, Ga., USA, 2007). The decoupling of these modes for electroded plano-convex surfaces forces all of the energy of the driving acoustic wave to the center with minimal energy trapping extending out to the crystal edge. As a result, the Q-factor and mass sensitivity is higher, by a factor of two, for the plano-convex resonator compared to the plano-plano (M. D. Ward and E. J. Delawski, “Radial mass sensitivity of the quartz crystal microbalance in liquid media.” Analytical Chemistry, vol. 63, pp. 886-890, 1991). Reduction of the anisotropic effects would be observed using the plano-convex surface with the concentration of the energy within a small active area at the center of the resonator. However, an increase in Q-factor prompts a narrowing of the mass sensitivity distribution which would make achieving a uniform mass sensitivity distribution potentially difficult. The broad-distribution indicative of the plano-plano quartz resonator is inherently capable of producing the bimodal profile necessary to achieve uniformity over a large sensing area.